The letters GTY on a cruise ticket stand for guaranteed--meaning a minimum standard room guarantee at a guaranteed minimum price. Passengers with GTY on their ticket will receive their cabin and deck number assignment around the time of check-in.
Cruise lines advertise a limited number of cabins at a low cost to entice passengers. A little-known fact is after these low-rate cabins sell out, cruise ships will often continue booking such deals if asked.
Those buyers receive a GTY, or a guarantee cabin type at a guaranteed price. If no more cabins are available in that category, passengers receive an upgrade to the next available category.
The only downside is this: if the bargain room is available (due to cancellations or miscalculations), GTY passengers will get what they paid for.